Reviews: SPALS: Fast Alternating Least Squares via Implicit Leverage Scores Sampling

As the "LS" of ALS suggests, each iteration of ALS for tensor decomposition amounts to solving a least squares regression problem. The main contribution of this submission is then to observe that good upper bounds on the leverage scores of the underlying matrix can be quickly approximated due to special structure of the matrix, namely Theorem 3.2 of the submission. This is the only, albeit important, novel observation of this paper. Once Theorem 3.2 is obtained, filling in the other details is standard. From this one observation, they are able to compare quite favorably with [37] (see Figure (a) on page 8).